Bernice E. Rogowitz and Holly E. Rushmeier IBM TJ Watson Research Center, P.O. Box 704, Yorktown Heights, NY USA

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1 Are Image Quality Metrics Adequate to Evaluate the Quality of Geometric Objects? Bernice E. Rogowitz and Holly E. Rushmeier IBM TJ Watson Research Center, P.O. Box 704, Yorktown Heights, NY USA ABSTRACT Geometric objects are often represented by many millions of triangles or polygons, which limits the ease with which they can be transmitted and displayed electronically. This has led to the development of many algorithms for simplifying geometric models, and to the recognition that metrics are required to evaluate their success. The goal is to create computer graphic renderings of the object that do not appear to be degraded to a human observer. The perceptual evaluation of simplified objects is a new topic. One approach has been to use image-based metrics to predict the perceived degradation of simplified 3-D models 1 Since that 2-D images of 3-D objects can have significantly different perceived quality, depending on the direction of the illumination, 2 2-D measures of image quality may not adequately capture the perceived quality of 3-D objects. To address this question, we conducted experiments in which we explicitly compared the perceived quality of animated 3-D objects and their corresponding 2-D still image projections. Our results suggest that 2-D judgements do not provide a good predictor of 3-D image quality, and identify a need to develop object quality metrics. Keywords: computer graphics, geometric simplification, perception 1. INTRODUCTION Three dimensional computer graphics was once used primarily in specialized computer-aided design (CAD) systems, and offline rendering applications such as feature film production. Increasingly 3-D graphics is being used in widespread interactive, networked applications such as computer games and e-commerce. The representation and display of 3-D objects can require substantial computer resources. A critical issue in designing effective interactive systems is to find the minimum representation of a 3-D object that does not compromise the visual quality of the object when it is rendered in two dimensions. In this paper we address how to evaluate the quality of the representation of a 3-D object. To do so, we compare the degree to which a simplified object appears degraded relative to an original. In one condition, the observers judge the perceived quality of the simplified object by comparing static images of the object; in the other condition, observers compare animated sequences of the original and simplified objects rotating through an angle of 90 degrees Geometric Representation and Simplification A wide variety of numerical forms can be used to represent 3-D objects. For interactive applications however, the most widely used representation is triangle meshes since they can be displayed rapidly by computer graphics cards commonly available on personal computers. In the past, 3-D objects for games and other interactive applications were carefully designed to use small numbers of triangles. More recently, objects are modeled by sampling continuous representations designed in CAD systems, or by capturing physical objects using 3-D scanning systems. Typically CAD or scanned objects are over sampled. Simplification algorithms have been used to reduce the number of triangles. A review of simplification algorithms can be found in an article by Cignoni et al.. 3 In general, geometric metrics, such as maximum distance from the original unsimplified surface, are used to drive algorithms that reduce the number of triangles. Simplified models are produced by trial and error using different values of the geometric metric until the model judged to be of adequate visual quality with the least number of triangles is obtained. Recent algorithms have been designed based on the realization that ultimately the perceived quality of the object is the critical issue. Driving the simplification by the resulting 2D display of the object, image metrics, rather than geometric metrics, have been proposed. In particular, Lindstrom and Turk 4 have developed a simplification method driven by minimizing the root-mean-squared difference in images generated from a large number of views of the simplified object relative to the original object. The algorithm simplifies a shape for a particular surface color variation and reflectance. In all the views used in their algorithm, light coincident with the viewer is used. Further author information: (Send correspondence to B.E.R.) 1

2 1.2. Perceptual Evaluations of Geometric Representations Although many simplification algorithms take into account geometric measures that are related to perception, only two studies have appeared that document psychophysical experiments to evaluate object quality. Watson et al. 1 used naming times to study the quality of object representations. Observers were presented with images of objects that had been simplified to various extents, and the time it took for observers to name the objects was recorded. Generally naming times correlated poorly with both geometric measures and image-based measures. In one condition however the authors found a correlation between naming time and the output of a perceptually-based image quality metric. This suggests a role for image-based metrics for evaluating geometric object quality. Rushmeier et al. 2 studied the effectiveness of replacing geometric detail with texture maps as a method of simplification. Observers were asked to rate the quality of match between high resolution models and various simplifications of the model. Consistent results were obtained across observers. For the simple objects used, it was found that the effectiveness of textures to replace geometric detail depended on the spatial detail of the object. In both of these studies, the authors assumed that the quality of still images can be used to assess the quality of an object representation. Since one essential feature of an interactive application is that objects are observed in motion, we wonder whether the perceived quality of 2D projections correlates with the perceived quality of the rotating object. It may be that the requirements for the representation of an object in motion may be reduced because the observer is able to detect less detail in frames that pass quickly. On the other hand, motion may make some artifacts in simplified objects more apparent if they result in unnatural jumps between frames. If the observer s judgements are the same for animations and for the still images that the animations are composed of, asking observers to rate comparisons of animations may be a more efficient method of examining object quality in future experiments. 2. DESIGN OF EXPERIMENT In general, 3-D objects have varying color and surface finish. To narrow the scope of this experiment, we considered only gray objects with a uniform surface finish. We used objects from the Georgia Tech Large Model database, that were originally obtained using 3-D scanning by researchers at Stanford University. In addition to being publically available, these models are of interest because they are commonly used in comparisons of geometric simplification algorithms by the computer graphics community Preparation of Stimuli The two objects used were the models bunny b and happy Buddha h in the database. The models are shown in Figs. 1, 2 and 3. The highest resolution model for the bunny was composed of 69,451 triangles, and for the Buddha 143,206 triangles. Two simplified versions of each model were generated using the Simplify module in the OpenDX open source visualization system. The Simplify module uses Gueziec s simplification method 5 that specifies a bound on the distance of each vertex in the simplified model as a percentage of the diagonal of a rectangle bounding box (BB) for the original model. For the bunny an error bound of 0.4 per cent of the BB diagonal produced a simplified model of 6467 triangles, and a bound of 1.0 per cent produced a very simplified model of 1679 triangles. The three versions of the bunny model viewed and lit from the front are shown in Fig. 1. For the happy Buddha bounds of 0.25 and 1.40 percent of the BB diagonal produced simplified and very simplified models of 27,168 and 6389 triangles respectively. The three happy Buddha models are shown in Fig. 2. For each model and level of simplification two sequences of 15 images were produced, one with a light collocated with the view position, as in Figs. 1 and 2, and one with the light directly above the object. In each sequence the object rotated in 5 degree increments from a front to a side view. Examples of side views of the models lit from above are shown in Fig. 3. The image sequences were assembled into animations to be played back at a rate of 15 frames/second, giving a smooth rotation from front to side that could be run in a forwards/backwards loop Procedure There were 8 basic conditions: two objects (bunny and happy Buddha), each at two levels of simplification (simplified and very simplified), with each level of simplification viewed under two lighting conditions (lit from above or from the front). We will refer to these conditions by specifying object-simplification-lighting, e.g. bva refers to the bunny model, very simplified lit from above. The experiment consisted of two parts. In the first part the observers were asked to rate the images of the simplified and very simplified models relative to images of the full resolution model under corresponding view and lighting conditions. The images were presented pairwise (full and simplified resolution in each pair) in random order (model types, simplification 2

3 Figure 1. Three versions of the bunny b model were used. On the left is the full resolution model, in the center the simplified model, and on the right the very simplified model. All three versions are shown here viewed and lit from the front. Figure 2. Three versions of the happy Buddha h model were used. On the left is the full resolution model, in the center the simplified model, and on the right the very simplified model. All three versions are shown here viewed and lit from the front. Figure 3. Sequences of each model were generated rotating from a front to a side view. Two sequences were constructed of each of the three models. They were either lit from the front and viewed from the front, as in Figs. 1 and 2, or lit from the top and viewed from the front as shown here. 3

4 levels and light conditions all mixed) to each observer in an html form. The observer rankings were indicated on an integer scale of 0 (worst) to 10 (perfect) using radio buttons under each test stimulus. For each of the 8 basic conditions images were generated for 15 different view positions, for a total of 120 image comparisons to be made by each observer. The observers were free to view all of the images to be compared before assigning scores, to determine their own calibration for worst comparison. Ten observers with normal or corrected to normal vision participated in the experiment. All were professionals at the Watson Research Center, but naive to the purpose of the experiment. In the second part of the experiment the observers were presented animations of the objects. They were asked to judge the quality of each animated simplified object relative to the full resolution animated object under the same lighting condition. The animations for each comparison were embedded in a Lotus Freelance presentation file to allow the observers to view the animations for as long as they desired without being able to stop the animations and examine individual frames. The animations for each comparison were viewed in succession, rather than side by side. As in the image comparisons, the observers were free to review the animations as many times as they wanted, and to go back a review previous pairs of animations before recording their final scores. 3. RESULTS Ten observers judged the degree to which a simplified geometric object matched the perceived image quality of the original object and assigned a rank to the perceived quality. The higher the rank, the greater the perceived similarity between the original and simplified object. This judgment was made for two different geometric objects, under two different illumination conditions, for a sequence of still images, and for an animated set of sequences Analyzing Data from Rating Experiments The data from these experiments are rank judgments. Observers use numerical values on a scale from 0 to 10, and these judgments provide a measure of perceived quality. These judgments are ordinal. Consider three still images rated 2, 5 and 8. These values are ordered, the images increase in perceived image quality, but the distances between these judgments do not necessarily represent perceptual distances. That is, although the number assigned to the highest quality image is four times the number assigned to the lowest quality image, its perceived image quality is not necessarily four times as great. Since these are ordinal, not nominal data, we cannot simply use mean rating scores to summarize the data, and must instead treat the data as ranks. We can compute, instead, statistical summaries appropriate to ordinal data, such as the proportion of scores at or above a certain value, rank-order correlations, etc. We call this out explicitly since it is a common practice to simply compute means and standard errors for rating data. Since these methods assume that the data are interval, using them on ordinal data can lead to biases in data interpretation The Perceived Quality of Simplified Objects Figure 4a shows results for one observer from one of the test patterns, hsa (happy Buddha, simplified, lit from above). The graph shows the rating score for each of the 15 viewing positions, plus, at the value indicated by A the score representing the degree of degradation of that target, relative to its original, when animated. Figure 4b shows the results for all 10 observers. Observations for two of the observers have been connected by lines to aid in visualizing the data. These data reveal the large variability in the observers rating responses. For this target, rating scores ranged from 2 to 8. Whatever effect there might be of viewing position, it is small relative to the variability in the data. Since we found no systematic effect of viewing position, we combined the rating scores for the 15 different viewing positions. Figure 5 shows a set of histograms representing quality scores under each of the eight conditions. Each histogram represents rating scores for ten observers at 15 different viewing positions (150 scores). The first column shows histograms; the second column shows cumulative histograms. The histogram representing the data hsa in Fig. 4 are in the fifth row. Images of the test objects are provided to aid in interpretation. For ease of viewing, the histograms have been ordered by mean rank score. Ordering them by the percentage of scores at or above the rank of 6 produces the same ordering. Several results emerge from this plot. First, for all targets, independent of lighting, the more simplified the object, the greater the perceived degradation. Second, the simpler model, the bunny, was less sensitive to degradation than the more complex model, the happy Buddha. When compared with its original, the bunny was systematically rated as being less degraded, independent of lighting angle. Third, in three of the four cases, the object lit from above was rated less positively than the same object, at the same simplification, lit from the front. In the cumulative histograms, the distribution of scores shifts to the right with higher scores when the object is lit from the front. 4

5 Figure 4. Example results for the target hsa (happy Buddha, simplified, lit from above). Fig. (a) shows the rating results for a single observer at each of 15 position of the object, and the score assigned to the quality of hsa when animated relative to the (animated) original, A. Fig. (b) shows the results for all observers for hsa. Figure 5. Histogram results for all eight conditions in the still image experiment. The first column on the left shows histograms, the second column shows cumulative histograms, and images representing each condition are shown on the far right. 5

6 Figure 6. Charts showing the percentage of trials with high image quality (% scores >= 6) for the 8 conditions. Fig. (a) shows the results for the still images, Fig.(b) shows the results for the animations Effects of Lighting Direction on Perceived Quality Figure 6 summarizes the effects of lighting on the perceived degradation of simplified objects. As a dependent measure, we compute the proportion of total trials where the simplified object is rated as having good quality relative to the original (% scores >= 6). The light bars indicate those conditions in which the object is lit from above; the dark bars indicate those conditions in which the object is lit from the front. The chart to the left shows data when judging 2-D images of the objects and provides a summary of the data in figure 5. Each bar represents the percentage of trials across observers (10) and positions (15), n =150, rated >= 6. The chart to the right shows data when judging animations of the 3-D objects. Each bar represents the percentage of trials across observers (n =10) rated >= 6. In Fig. 6b we see that the quality judgments made for animations of 3-D objects are in some ways similar to those made for their 2-D projections. For example, the very simplified models receive systematically lower scores than their less simplified counterparts. The greater robustness of the bunny model relative to the happy Buddha however is not replicated, and most strikingly the effects of lighting are quite different for the better quality (less simplified) models. In particular the superiority of lighting from the front is much more pronounced for the simplified happy Buddha model hs. Lighting from above produces comparable results, but under animation lighting from the front produces a considerably higher proportion (80 %) positive scores. That is, the visual effects produced by simplification are reduced under lighting from the front when that object is animated. Under animation, the perceived quality of the object when lit from the front, is increased Geometric Metrics and Perceptual Quality Figure 7 explores the degree to which a standard computer graphics metric for measuring object simplification captures the perceived quality of these objects. Here rated quality is plotted as a function of a standard measure of object degradation. The lower the maximum distance as a percentage of the bounding box, the less distortion. If this measure captures perceived quality, then the quality rating scores should decrease linearly with this measure, and there should be no difference between objects lit from above and those lit from the front. In this figure, we consider the results of the two experiments separately. The results are remarkably similar. Whether the judgments are made on static 2-D images or animated 3-D objects, perceived quality decreases monotonically and linearly for models lit from the front. For front lighting r 2 is ;0:98 for still images and ;0:95 for animated sequences. However perceived quality is not monotonic for models lit from above. The large difference between the two lighting conditions, suggests that a purely geometric description will not be adequate to describe these results. As with the still images, the perceived quality of 3-D animated geometric objects depends critically on the incident angle of the lighting Object and Image Quality In our experiments, we measured the degree to which animated objects and their 2-D image projections were degraded perceptually by geometric simplification. In order to use an image-based quality metric to describe the perceived degradation of a 6

7 Figure 7. Perceptual ratings versus a standard geometric metric for simplification, the maximum distance of the simplified geometry from the original as a percentage of bounding box diagonal. Fig. (a) shows the ratings for the still images, (b) shows the ratings for the animations. Although perceived quality is linear with this metric with lighting from the front, it is not even monotonic with lighting from above. Furthermore, this metric does not account for differences between lighting conditions. Figure 8. Comparisons of the ratings of the still and animated cases. The proportion of trials in which the still image is given a higher score than the animated object is shown by the light bars, and the proportion of trials in which the still image is given a lower score is shown by the dark bars. 7

8 3-D object, we would need to show that the degree of perceived degradation of the still image is comparable to the perceived degradation of the animated object. Figure 8a explores this hypothesis. Instead of counting the percentage of good scores, we count the proportion of trials when the still image was given a higher score than the animated object and the proportion of trials when the still image was given a lower score. If the degree to which geometric simplification degrades perceived quality is the same for images and animations, then we expect the proportion of lower and higher scores to be the equal. For example, if an observer assigns a rank of 6 to an animated object, then the expected value for the 2-D projections should also be 6, with an equal proportion of scores above and below this expected value. In Fig. 8, the light bars show the proportion of the still images trials rated higher than the animated object; the dark bars show the proportion of trials where the still images were rated lower in quality than the animated object. In this chart, we see that for three of the test stimuli, the still images are consistently rated lower than the animated object (dark bars smaller); for three of the stimuli, the still images are consistently rated higher in quality than the animated object. For two of the stimuli, the perceived degradation due to the geometric simplification is the same, whether the observer is rating the images or the animation. It is clear that the degree of perceived degradation of the still images does not adequately predict the perceived degradation in the equivalent animated images. 4. CONCLUSIONS In these experiments, we explored the perceived quality of two different representations of 3-D objects, in order to better understand how to characterize and measure the effects of geometric simplification. To do so, we selected a simple and a complex geometric model, Bunny and Happy Buddah, and created two simplified versions of each. We used these stimuli to study the effect of geometric simplification on perceived quality by having observers rate the quality of these stimuli relative to their unsimplified originals. Since, in previous experiments, we had observed striking differences in the quality of 2-D images of 3-D objects depending on the direction of the lighting, we varied lighting explicitly, making all measurements with lighting from above and with lighting from the front, aligned with the observers viewing direction. Although geometric measures of model simplification are based on the 3-D geometry of those models, the two existing experiments aimed at developing a more perceptual model were based on the evaluation of 2-D projections of those objects. In particular, it had been suggested that the quality of 3-D objects could be predicted based on the quality of static 2-D projections. To explore this hypothesis, we conducted our experiments under two different conditions. In the first condition, the observers rated the quality of 2-D static images, 15 projections of the 3-D object, at 5-degree angles along a quarter-rotation from side-to-front view. In the second condition, the observers rated an animated sequence of these 15 images, showing the object rock back and forth from side-to-front-to side. When compared with the unsimplified original, the more the object was simplified, the lower the rating scores, for both animated and static presentations. Perhaps the most striking result of these experiments is the remarkable effect of lighting on perceived quality. In 7 of the 8 conditions tested, judgments of perceived quality depended on the direction of the lighting. Furthermore, the degree to which lighting direction affected the quality judgments depended on whether static or animated images were being judged. For the two more complex objects, the simplified Buddah (hs) and the simplified Bunny (bs), the perceived quality of the rendering increased significantly when the object was animated, if that object was lit from the front. That is the degree of geometric simplification was much less noticeable in animation for simplified objects lit from the front. This suggests that certain simplified geometric objects might be best lit from the front, rotating. Since the human visual system is less sensitive to high spatial frequencies when an object is moving, it may be that the rotation reduces the detectability of high spatial frequency artifacts introduced by the simplification process. This result may not be observed when the object is lit from the front, since the contrast of these artifacts is so high that their effect cannot be effectively attenuated. It would be interesting to explore this idea further by explicitly varying the spatial and temporal frequency composition of the stimuli. Since one goal of this work is to develop a metric for characterizing the perceived quality of geometrically simplified graphical objects, we examined the perceptual rating scores as a function of a standard metric for characterizing the geometric effect of simplification, the maximum distance of the distortion as a percentage of the bounding box. We found that for objects lit from the front, perceived quality decreased linearly with this measure of geometric difference. Rated quality did not decrease monotonically for these same objects when lit from above. According to this metric, the simplified happy Buddah (hs), with %BoundingBox =0:27 should have much higher perceived quality than the simplified bunny (bs), with %Boundingbox = 0:4. Instead, we found for both static and animated viewing conditions, the opposite was true. The hs stimulus had consistently lower scores, indicating much lower perceived quality. 8

9 Perhaps the most important observation to make regarding the geometric metric is that it does not predict any difference between the two lighting conditions. Since the geometry of the object is unchanged when the lighting direction is changed, the metric sees these as identical. Perceptually, however, lighting direction is a critical factor in judging the amount of distortion produced by the simplification. An important criterion for selecting a metric is that address the difference between the perceived quality of still and animated images. This difference is not a simple shift in sensitivity that can be accounted for with a normalization factor. In some cases, the static images were consistently rated higher in quality than the animated sequence; in some cases the static images were consistently rated lower than the animated sequence. The pattern of these results is not straightforward, and more work needs to be done. The clear conclusion, however, is that even if we had a metric that completely characterized the perceived quality of static 2-D projections of 3-D objects, this metric would not predict the quality of 3-D animated sequences of those same images. REFERENCES 1. B. Watson, A. Friedman, and A. McGaffey, Using naming time to evaluate quality predictors for model simplification, in Proceedings of ACM SIG CHI Conference, pp , H. Rushmeier, B. Rogowitz, and C. Piatko, Perceptual issues in substituting texture for geometry, in Proc. SPIE Human Vision and Electronic V, vol. 3959, pp , P. Cignoni, C. Montani, and R. Scopigno, A comparison of mesh simplification algorithms, Computers and Graphics 15(1), pp , P. Lindstrom and G. Turk, Image-driven simplification, ACM Transactions on Graphics 19, pp , A. Gueziec, Locally toleranced surface simplification, IEEE Transactions on Visualization and Computer Graphics 5, pp , P. Engeldrum, Psychometric Scaling: A Toolkit for Imaging Systems Development, Imcotek Press, Winchester, MA,

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